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SCCDFTB as a bridge between MM and high-level QM.

SCCDFTB as a bridge between MM and high-level QM. Jan Hermans University of North Carolina. 1. From QM to MM via SCCDFTB. 1. SCCDFTB better than MM Examples Simulation of crambin (Haiyan Liu) Simulation of “dipeptides” (Hao Hu) b. But why?

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SCCDFTB as a bridge between MM and high-level QM.

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  1. SCCDFTB as a bridge between MM and high-level QM. Jan Hermans University of North Carolina 1

  2. From QM to MM via SCCDFTB 1. SCCDFTB better than MM • Examples Simulation of crambin (Haiyan Liu) Simulation of “dipeptides” (Hao Hu) b. But why? Concerted changes of geometry in N-methyl acetamide Hydrogen bonding between two N-methyl acetamide molecules More flexible 2. Develop and test MM force fields 2

  3. From QM to MM via SCCDFTB Simulation of crambin (Haiyan Liu; 2001) Liu, HY, Elstner, M, Kaxiras, E, Frauenheim, T, Hermans, J, & Yang, W. Quantum mechanics simulation of protein dynamics on long time scale. Proteins, 44: 484-489, 2001. Improved agreement of backbone geometryin folded state Simulation of “dipeptides” (Hao Hu; 2002) Hu, H, Elstner, M., Hermans, J. Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of how to model the unfolded peptide backbone in solution. Proteins, 50, 451-463 (2003). Improved agreement of backbone geometryin solution 3

  4. SCCDFTB Ace-Ala-Nme in explicit water Hao Hu, 2002 amber, charmm, gromos, opls-aavs. each other and vs. SCCDFTB 4

  5. Why better accuracy with SCCDFTB?SCCDFTB reproduces concerted changes of geometry charge fluctuations hydrogen bond geometryexample: N-methyl acetamide 5

  6. planar C-N-CA2 H-N-CA2 H-N-C tetrahedral Concerted changes of geometry inN-methyl acetamide, CH3-NH-CO-CH3 Recipe: 1. Twist about NH-CO bond 2. Minimize the energy (with SCCDFTB) 6

  7. Fluctuation of charge in N-methyl acetamide atom: C O N HN w =180º (energy minimum) 0.4911 -0.5082 -0.2504 0.1879 w = 90º (saddle point) 0.5255 -0.4257 -0.3343 0.1749 Fluctuations of charges and geometry are coupled 7

  8. NHO prefers 180º  HOC likes 130º Non-spherical electron distribution: C=O interacts with H-N Non-linear N-H…O=C hydrogen bonds Cf. Side chain hydrogen bonds in proteins and by ab initio QM: Morozov, Kortemme, Baker 8

  9. Distribution of COH in dimers of N-methyl acetamide. SCCDFTB MM force field SCCDFTB favors bent arrangement Simple Point Charge model of MM favors linear structures Hermans, J. Hydrogen bonds in molecular mechanics force fields.Adv. Protein Chem. 72, 105-119, 2006. 9

  10. But … SCCDFTB is too flexible: 1. Correlation of DFT (B3LYP/631G*) and SCCDFTB energies 1000 conformations from 1 ns MD simulation with SCCDFTB 10

  11. SCCDFTB is too flexible: 2. Energy profile for internal rotation in butane DFT B3LYP/631G*: eclipsed: DE =±120 = 3.35 gauche: DE= ±60 = 0.83 cis: DE=0 = 5.69 SCCDFTB: eclipsed: DE =±120 = 2.57 gauche: DE= ±60 = 0.45 cis: DE=0 = 3.80 (relative to trans,  = 180) MP2: eclipsed: DE =±120 = 3.31 gauche: DE= ±60 = 0.62 cis: DE=0 = 5.51 11

  12. End of part 1

  13. Molecular mechanics energy function: how to improve it? intramolecular non-bonded 1. How precise is this expansion? 2. How accurate is this model? 3. How accurate are the implementations (amber, charmm, … 13

  14. Assume a high-level QM method as “REALITY”: DFT (B3LYP/631G*) Try to reproduce its energy. (can always choose a higher level of QM.)

  15. Recipe STEP 1: 1. Simulate (1 ns with SCCDFTB) 2. Save 1000 conformations Example: methane, CH4 Recipe STEP 2: 3. Compute Epot with B3LYP/631G* 4. Fit* a new MM forcefield 5. Compute Epot with the new MM force field * By minimizing the RMS deviation The slope is very close to 1 The RMS deviation is 0.07 kcal/mol (mean dEpot = 3) 15

  16. What are the most important energy parameters for methane? rms residual Standard quadraticMM terms not very useful include these terms (not needed in simulationswith fixed bond lengths) precision 16

  17. Systems studied to date (manuscript): “rigid” molecules methane, benzene, water molecules with internal rotation ethane, propane, butane, methyl-benzene Non-bonded interactions methane…methane, ethane…ethane water…methane, water…water Some results and some conclusions …. 17

  18. LESSONS LEARNED: Geometric parameters agree well. Transferability between related molecules Compared with “standard” force fields 18

  19. Coulomb interactions: (we skipped a slide) (Water: Fixed Point charges based on ESP inadequate) Methane and ethane: ESP charges can be used Methane and ethane:Lennard-Jones repulsive parameters Conclusion: Nice agreement

  20. LESSONS LEARNED: Geometric parameters agree well. Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…methane 21

  21. LESSONS: LESSONS LEARNED: Geometric parameters agree well. Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…methane Intermolecular parameters for methane and ethane are similar (and FPC model is OK). 22

  22. LESSONS: LESSONS LEARNED: Geometric parameters agree well. Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…methane Intermolecular parameters for methane and ethane are similar (and FPC model is OK). Exponent of L-J repulsive term = 12 is good. 23

  23. H H C C Butane: “intrinsic” torsion term non-bonded interactions (1/r12 and 1/r) 1-4 C,C 1-5 and 1-4 C,H 1-6, 1-5, 1-4 H,H • * In the SCCDFTB simulation forced 360º rotation about C2-C3, <dE> = 14 kcal/mol • * Fit several MM models: • A0* has 38 parameters, r = 0.441 • A5 has 12 parameters, r = 0.598 24

  24. Butane: Fit for model A5 25

  25. Butane: • * Simulate butane with A5 force field (and 2 others) • Calculate PMF for torsion about C2-C3 Critical tests: * Re-calculate DFT (B3LYP/631G*) energies * Compare energies at minima and barriers DFT vs. A5 (and 2 others) 26

  26. Simulation with A5 force field red curve = MM energy black dots = DFT energy black curve = PMF DFT energy issystematically high 27

  27. Slope of best fit is 1.04 28

  28. With more parameters (np) in the MM force field: The slope goes down to 1.02 The PMF becomes a little bit sharper Energies andfree energiesat minima and maxima (relative to minimum at  = 180º) Slope and rmsd of correlation between DFT and MM energies 29

  29. LESSONS: LESSONS LEARNED: Geometric parameters agree well. Fixed point charge (FPC) model for Coulomb energy is poor for water…water and water…methane Intermolecular parameters for methane and ethane are similar and FPC model is OK. Exponent of L-J repulsive term = 12 is good. Torsion in ethane, propane, butane:omit terms in 1/r“messy” set of 1-4, 1-5 and 1-6 repulsive terms 30

  30. Why is SCCDFTB important in this project: • Fast to run • Easy to set up (need only coordinates) • Equilibrium geometry agrees well with DFT • Slightly more flexible: do not miss anything

  31. Future work: I hope so Thanks to • Weitao Yang • Hao Hu (coauthor of paper) 32

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